Physical Review E

Vertical transmission of an infectious disease from parent to offspring is a common transmission route in many systems. Here we investigate the dynamics of a pathogen with both horizontal and vertical transmission within a spatially structured population. We introduce a lattice model with a pair approximation that includes both local and global transmission and reproduction. We find that vertical transmission can determine pathogen invasion and reduce the horizontal transmission rate required for invasion. When the majority of transmission and reproduction is local, vertical transmission can destabilise a host population to cause limit cycles. Given the advantages of a pathogen having both horizontal and vertical transmission routes, we extend the model to investigate the likelihood a mutant strain with both transmission modes will outcompete a resident strain with only horizontal transmission. When there is no trade-off the mutant always invades and when there is a trade-off with horizontal transmission, the mutant emerges when the cost to the horizontal transmission rate is not too large. Depending on how the mutant appears within the host population, it may have an initial advantage over the resident strain even if it cannot outcompete in the long-term. Our work demonstrates the potential importance of vertical transmission within host-pathogen dynamics.

A key component of intraneuronal communication is the modulation of postsynaptic firing frequencies by stochastic transmitter release from presynaptic neurons. The time interval between successive postsynaptic firings is called the inter-spike interval (ISI), and understanding its statistics is integral to neural information processing. We start with a model of an excitatory chemical synapse with postsynaptic neuron firing governed as per a classical integrate-and-fire model. Using a first-passage time framework, we derive exact analytical results for the ISI statistical moments, revealing parameter regimes driving precision in postsynaptic action potential timing. Next, we extended this analysis to include both an excitatory and an inhibitory presynaptic connection onto the same postsynaptic neuron. We consider both a fixed postsynaptic-firing threshold and a threshold that adapts based on the postsynaptic membrane potential history. Our analysis shows that the latter adaptive threshold can result in scenarios where increasing the inhibitory input frequency increases the postsynaptic firing frequency. Moreover, we characterize parameter regimes where ISI noise is hypo-exponential or hyperexponential based on its coefficient of variation being less than or higher than one, respectively.

The spatial structure of populations may promote the emergence and maintenance of cooperation. Cooperation in the prisoners dilemma is favored under specific update rules in evolutionary graph theory models with one individual per node of a graph, but this effect vanishes in models with well-mixed demes connected by migrations under soft selection. In contrast, experiments and models involving cycles of growth, merging and dilution have shown that spatial structure can favor cooperation. Here, we reconcile these findings by studying deme-structured populations under growth-merging-dilution dynamics, corresponding to a clique (fully connected graph) under hard selection. We obtain analytical conditions for the cooperator fraction to increase during deterministic logistic growth, and to increase on average under dilution-growth-merging cycles, in the weak selection regime. Furthermore, we analytically express the fixation probability of cooperators under weak selection, yielding a criterion for cooperative mutants to have a higher fixation probability than neutral ones. Finally, numerical simulations show that stochastic growth further promotes cooperation. Overall, hard selection is essential for cooperation to be promoted in deme-structured populations.

Exploring the emergence of spatio-temporal patterns due to nonlinearities in gene expression is a relatively new development. In this work, we explore the effect of resource constraint on gene regulatory motif from both equilibrium and spatio-temporal standpoint, taking into consideration the degradation class of resource, protease. We have demonstrated that protease-tagged degradation can cause an emergent bistability to form in the system in a steady-state scenario. Instead of a graded linear response in protein synthesis, two Saddle-node bifurcations caused by protease competition provide a switch-like response with hysteresis, where two drastically differing protein concentrations can coexist. We next turn our attention to spatio-temporal analysis: we extend our study for a two-dimensional sheet of cells with diffusible protein molecules and report the stationary patterns.To investigate the reasons behind these non-homogeneous stationary patterns, we investigate the traveling wave solution and observe that a stationary pattern is formed by the traveling wave solution. Considering that proteases play a major role in the regulation and expression of genes in a variety of diseased scenarios, the repercussions of this spatial patterning caused by protease competition can be extensive in gene regulatory systems.

One of the most critical steps in human reproduction is the selection of the dominant follicle when a single follicle is chosen from a large group of follicles to ovulate. Although this process involves complex hormonal regulation, the complete microscopic picture of unique selectivity remains unclear. We propose a novel stochastic mechanism for dominant follicle selection that incorporates the actions of the most relevant hormones, follicle-stimulating hormone (FSH) and estradiol. Our theoretical picture suggests the following sequence of events. As soon as the FSH concentration reaches the critical threshold, one of the available follicles is randomly selected, which immediately stimulates the production of estradiol, which, via a negative feedback mechanism, suppresses further FSH production, lowering its concentration below the critical threshold. This suppression limits the time window for the possible second follicle selection event, allowing only a single follicle to be selected. Based on this picture, a minimal quantitative theoretical model of dominant follicle selection is developed and analyzed using analytical calculations and computer simulations. Theoretical analysis shows how the interplay between different parameters that govern follicle selection leads to high selectivity. Our theoretical approach can explain some key known observations, providing a quantitative tool for analyzing biological reproduction phenomena.

The environments inhabited by flying insects demand a balance between flight efficiency and flight manoeuvrability. In structural oscillators such as the insect indirect flight motor, efficiency (arising from resonance) and manoeuvrability (arising from kinematic modulation) are typically quid pro quo, with modulation incurring penalties to efficiency. Band-type resonance is a phenomenon that offers, in theory, a strategy to lessen these penalties via careful navigation through a band of efficient kinematic states. However, identifying this band is challenging: no methods exist to identify the complete band in realistic motor models, involving elasticity distributed across thorax and wing. Nor are the effects of elasticity distribution on the band known. In this work, we address both open topics. We present a suite of numerical methods for identifying the complete resonance band in general systems. Applying them to models of the insect flight motor with distributed elasticity--thoracic and wing flexion--reveals that distributed elasticity is moderate-risk but high-reward morphological feature. Well-tuned distributions expand the resonance band over fourfold whereas poorly-tuned distributions completely extinguish the resonance band. These results indicate that distributing elasticity across the insect flight motor can have adaptive value, and motivate broader work identifying distributions across species.

Cell-cell adhesion is a key regulator of cancer invasion. In this work, we extend a pre-existing individual based cancer invasion model by introducing a stochastic representation of N-cadherin-mediated adhesion, where the lifetime of a cell-cell bond depends on the pulling force acting on the bond. Using experimental data, we derive expressions for the mean and standard deviation of N-cadherin bond lifetimes and fit them to Gamma distributions, enabling their treatment as force-dependent random variables. These distributions are then used to modify the diffusion coefficient of mesenchymal cancer cells. The model predicts reduced random motility with increasing adhesion and incorporates a dynamic transition between catch- and slip-bond behaviour. Along with this model for cell motility, we propose a preliminary physical framework, that can be used to model pattern formation as a result of the new adhesion mechanic.

Dynamical processes on complex networks have a long history of study with increasing applications across many fields. While epidemics in heterogeneous networks have received much attention in terms of how connectivity patterns drive epidemic outbreaks, affect critical thresholds, timescales, final outbreak size and immunization efforts, less attention has been devoted to endemic multi-strain scenarios and questions of selection and coexistence dynamics. Here, we provide an SIS framework for multiple co-circulating strains and co-infection, which can be reduced to a replicator dynamics on a host contact network. Using the analytical tractability of the replicator formalism, we study how network heterogeneity affects multi-strain dynamics, and compare its effects relative to the homogeneous contact distribution, identifying key relevant metrics for comparison. In particular, the pairwise invasion fitness matrix comparison reveals that higher network heterogeneity acts to increase the speed of multi-strain dynamics and typically tends to have stabilizing effects that reduce the number of coexisting strains. While many aspects of the replicator dynamics remain complex to study, especially for high number of strains, the advantage of this model representation lies in the dimensional reduction of a huge system, enabling general, more direct and efficient numerical computations. Furthermore the explicit bottom-up constitution of crucial parameters yields biological and epidemiological insight for critical system transitions across macroscopic gradients and can be used to guide interventions.

In microbial populations, fitness, which is essential to understand and predict evolution, is often defined and measured as the net growth rate of a population in isolation. Applying the same definition to viruses is challenging, both because viral replication involves a host infection process, which is determined by several parameters that are context-dependent, and because viruses compete heavily for resources (susceptible cells). These challenges are particularly exacerbated in spatial range expansions, where multiplicity of infection is often high and resource availability varies in time and space. To assess different fitness definitions and their generalizability, we investigate a model of coupled partial differential equations for phage plaque expansion in one and two dimensions. We find that two commonly used metrics for phage fitness in plaque expansions, i.e., steady state phage densities and front expansion speed in isolation, are unable to reliably predict the winner in one- and two-dimensional direct competitions. More generally, we find that optimal phage traits depend on the dimensionality of the system and the make-up of the phage population, leading to unexpected behaviours, e.g., rock-paper-scissor dynamics and, in high dimensions, enhanced phage density due to the nearby presence of a competitor. We show that the phenomenon stems from the interplay between resource consumption and replication and thus may apply more broadly to any population competing for shared resources.

Voltage perturbations to a repetitively firing Hodgkin-Huxley (HH) model of neuronal spiking in the bistable regime with coexisting limit cycle and stable steady node can either lead to the spikes phase resetting or collapse to the stable steady state. The latter describes a non-firing hyperpolarized quiescent state of the neuron despite the presence of constant external current. Using asymptotic phase response curve (PRC), the impact of voltage perturbations on a repetitively firing HH model is studied here while it is diffusively coupled to another HH model under identical external stimulation. It is observed that the pre-perturbation state of synchronization and the coupling strength critically determine the PRC response of the perturbed HH dynamics. Higher coupling strengths of perfectly in-phase (anti-phase) synchronized HH models shrink (expand) the combinatorial space of perturbation strengths and the oscillation phases causing collapse to the quiescent state. This indicates reduced (enlarged) basin of attraction, viz. the null space, associated with the steady state in the HH phase space. The findings bear important implications to the spiking dynamics of diverse interneurons, as well as special cases of pyramidal neurons, coupled through electrical synapses via. gap junctions, and suggest the role of gap junction plasticity in tuning vulnerability to quiescent state in the presence of biological noise and spikelets.

We describe an approach for analyzing biological networks using rows of the Krylov subspace of the adjacency matrix. Specifically, we explore the scenario where the Krylov subspace matrix is computed via power iteration using a non-random and potentially non-uniform initial vector that captures a specific biological state or perturbation. In this case, the rows the Krylov subspace matrix (i.e., Krylov trajectories) carry important functional information about the network nodes in the biological context represented by the initial vector. We demonstrate the utility of this approach for community detection and perturbation analysis using the C. Elegans neural network.

The actin cytoskeleton is an inherently disordered active system. the actomyosin cortex and reconstituted actomyosin systems are globally disordered, yet undergo transitions between distinct disordered states as parameters like motor and crosslinker concentration and filament length and rigidity change. In cells these changes are related to genetic mutations or differences in cell state and dictate fundamental biological processes. However, we dont have well established methods to detect and classify differences in disordered polymer networks. Image-based morphology techniques provide a non-invasive, high-throughput method of extracting information about a system. In this work we simulate biopolymer networks under varying conditions and develop and use morphological descriptors to construct trajectories in morphospace. Using statistical analysis we find that morphological descriptors are able to distinguish between different trajectories of the system, including differences not apparent to the eye. However, no single descriptor alone is able to capture all the differences in the simulated trajectories. Nematic order parameters typically perform the worst for our simulations while curvature and texture descriptors can collectively distinguish between dynamic trajectories. This work helps develop quantification of cytoskeleton dynamics for classification and data-driven modeling.

Imagine you walk in a plane. You move by making a step of a certain length per time interval in a chosen direction. Repeating this process by randomly sampling step length and turning angle defines a two-dimensional random walk in what we call comoving frame coordinates. This is precisely how Ross and Pearson proposed to model the movements of organisms more than a century ago. Decades later their concept was generalised by including persistence leading to a correlated random walk, which became a popular model in Movement Ecology. In contrast, Langevin equations describing cell migration and used in active matter theory are typically formulated by position and velocity in a fixed Cartesian frame. In this article, we explore the transformation of stochastic Langevin dynamics from the Cartesian into the comoving frame. We show that the Ornstein-Uhlenbeck process for the Cartesian velocity of a walker can be transformed exactly into a stochastic process that is defined self-consistently in the comoving frame, thereby profoundly generalising correlated random walk models. This approach yields a general conceptual framework how to transform stochastic processes from the Cartesian into the comoving frame. Our theory paves the way to derive, invent and explore novel stochastic processes in the comoving frame for modelling the movements of organisms. It can also be applied to design novel stochastic dynamics for autonomously moving robots and drones.

Evolutionary therapies regulate heterogeneous populations by altering selective pressures through treatment sequences in cancer and infections. This letter develops an invariant-set framework for treatment-induced containment based on positive triangular invariant sets. For periodically switched systems, sufficient conditions are derived for the existence of such invariant regions. Robustness with respect to mutation is established by showing that the invariant simplex persists under small perturbations of the subsystem matrices. In the two-phenotype case, the analysis yields an explicit mutation threshold that separates regimes in which therapy cycling maintains containment from regimes in which mutation can enable evolutionary escape. Simulations illustrate the geometry of the invariant sets and the role of mutation and dwell time in containment robustness.

Melanoma is a cancer of the melanocyte, known to have an ability to readily switch between different transcriptional cell states that convey different phenotypic properties (e.g. hyper-differentiated, neural crest-like). This ability is believed to underpin intratumour heterogeneity and plastic adaptation, which contributes to resistance to therapy and immune evasion of the tumour. Therefore, understanding the mechanisms underlying acquisition of transcriptional cell states and cell-state switching is crucial for the development of therapies. We model a minimal gene regulatory network comprising three key transcription factors, whose varying gene expression encodes different melanoma cell states, and use deterministic spatiotemporal differential-equation models to study gene-expression dynamics. We exploit an approximation, based on cooperative binding of transcription factors, in which the models are piecewise-linear. We classify stable states of the local model in a biologically relevant manner and, using a naive model of intercellular communication, we explore how a population of cells can take on a shared characteristic through travelling waves of gene expression. We derive a condition determining which characteristic will become dominant, under sufficiently strong cell-cell signalling, which creates a partition of parameter space.

A common assumption in molecular evolution is the fixed selection nature of a mutation, for instance, a neutral mutation is selectively neutral for all individuals who carry the mutation, and so forth a deleterious or beneficial mutation. Our recent work challenged this presumption, postulating that individuals with a specific mutation exhibit a fluctuation in fitness, short for FSI (fluctuating selection among individuals). Moreover, an intriguing phenomenon called selection-duality emerges, that is, a slightly beneficial mutation could be a negative selection (the substitution rate less than the mutation rate). It appears that selection-duality is bounded: the low-bound is the generic neutrality where the mutation is neutral by the means of fitness on average, while the up-bound is the substitution neutrality where the substitution rate equals to the mutation rate. In this paper, we conducted a thorough theoretical analysis to evaluate how many generations needed for a selection-duality mutation to be fixed in a finite population. A striking finding is that the mean fixation time of a selection-duality mutant, including the generic neutrality and the substitution neutrality, is approximately identical, which is considerably shorter than the case of strict neutrality without FSI. One may further envisage that the fast-fixation nature of selection-duality mutations could result in a considerable genetic reduction at linked sites.

The interactions of droplets and filaments can lead to mutual deformations and complex combined behavior. Such interactions also occur within the cell, where biomolecular condensates, distinct liquid phases often composed of proteins, have been observed to structure and affect the organization of the cytoskeleton. In particular, biomolecular condensates have been shown to undergo characteristic deformations when cytoskeletal filaments are fully embedded within them. However, a full understanding of the underlying physical mechanisms is still missing. Here, we combine experiments with coarse-grained molecular dynamics simulations and analytical models to uncover the physical mechanisms that define emerging shapes of droplets containing filaments. We find that the surface tension of the liquid phase and the bending energy of the filament(s) suffice to accurately capture emerging shapes if the length of the filament is small compared to the liquid volume. As the volume fraction of filament(s) increases, wetting effects become increasingly important, setting physical constraints within which surface and bending energies compete to define the droplet shapes. We find that mutual deformations of condensate and filament extend accessible shapes beyond classical stability considerations, leading to structuring and entrapment of contained filaments. Shape deformations may further affect ripening dynamics that favor certain geometries. Our findings provide a physical framework for a better understanding of the possible roles of biomolecular condensates in cytoskeletal organization.

Phase synchronized population dynamics of various species constituting a complex ecosystem elevates the risk of their extinction due to both environmental stochasticity and simulateneous low density fluctuations. Therefore, an extremely vital approach to measure the extinction risk of an ecosystem as a whole is to quantify the phase synchrony among the species populations co-habiting and interacting with each other in an ecosystem. Generally, in models describing population dynamics of ecosystems, both trophic and non-trophic inter-species interactions are modelled as interactions between two species. This approach contradicts the fact with such a large number of species living in close proximity, more than two species must partake in the same interaction influencing the population dynamics of each other. To address this, higher-order interactions need to be incorporated in the models describing population dynamics of an ecosystem. Consequently, their effect on phase synchronization of populations also need to be investigated. In this study, we model a species-rich ecosystem as a complex phase oscillator network and examine the phase dynamics of the total population. Each node of this network represents a constituent species, modelled as a Sakugachi-Kuramoto phase oscillator coupled non-linearly to the other nodes through both first-order and higher-order inter-species interactions. These interactions can be both mutualistic (positive) and antagonistic (negative) in nature. Along with the higher-order interactions, we also incorporate inherent asymmetry among the nodes to account for habitat heterogeneity. Further, we investigate the effects of both higher-order coupling and asymmetry on the phase synchronization of the total population. Our findings demonstrate that higher-order interactions above a threshold amplitude enforces a transition from synchronous to asynchronous dynamics of the ecosystem. Further, we find that increase in the size and diversity of the ecosystem leads to an increase in the threshold value of higher order coupling required to reach asynchronous dynamics. We also demonstrate that this higher-order induced asynchrony is further promoted by high asymmetry among the individual nodes. Importantly, negative inter-species interactions, if existing to a high degree also induce asynchrony in the system. Moreover, the size of the network also plays a role in deciding the threshold value of higher order coupling required to induce asynchrony.

Microbes constantly interact with their environment by depleting and transforming food sources. Theoretical studies have mainly focused on Lotka-Volterra models, which do not account for food source dynamics. In contrast, consumer-resource models, which consider food source dynamics, are less explored. In particular, it is still unclear what physical mechanisms control oscillatory dynamics at a single population level, a phenomenon which can only be captured by a consumer-resource model. Here, we present a minimalistic consumer-resource model of a single microbial population with growth and death dynamics, consuming a continuously replenishing substrate. Our model reveals that decaying oscillations can occur around steady state if and only if the timescale of microbial adaptation to food supply changes exceeds the death timescale. This interplay of timescales allows us to rationalize the emergence of oscillatory dynamics when adding various biophysical ingredients to the model. We find that microbial necromass recycling or complementary use of multiple food sources reduces the parameter range for oscillations and increases the decay rate of oscillations. Requiring multiple simultaneous food sources has the opposite effect. Essentially, facilitating growth reduces the likelihood of oscillations around a fixed point. We further demonstrate that such damped oscillatory behavior is correlated with persistent oscillatory behavior in a noisy environment. We hope our work will motivate further investigations of consumer-resource models to improve descriptions of environments where food source distributions vary in space and time.

Haar-like wavelets sparsify the phylogenetic covariance matrices of large, uniformly random k-regular trees with overwhelmingly high probability. This motivates the Haar-like distance, a {beta}-diversity metric that implicitly ranks the splits of a reference phylogeny by their relevance in differentiating two microbial environments, offering an interpretation as to why the environments differ compositionally. Nevertheless, uniform binary trees exhibit statistical features distinct from those of the trees used by practitioners, leaving the extent of sparsification and the practical validity of the implied Haar-like distance speculative. To address this, our manuscript examines the sparsification of phylogenetic covariance matrices of large critical beta-splitting random trees, a model introduced to better reflect real-world phylogenies. By obtaining sharp asymptotic estimates of the first and second moments of the external path length in this ensemble, we demonstrate that the Haar-like basis also pseudo-diagonalizes the phylogenetic covariance matrix of most large trees in this more realistic framework. Additionally, we devise a test to assess the statistical significance of splits in the reference phylogeny identified by the Haar-like distance. We apply the test to a well-studied microbial mat to further substantiate the presumption that the identified splits represent genuine biological signals differentiating the top and bottom layers of the mat.